What do I do if the other person ignores my boundaries?

You have the option of ending the relationship.
Boundaries are deal-breakers and the discomfort you feel when someone violates your boundaries makes sense.
You may choose to give the other person a few chances to learn to respect your boundaries. Remember that it's ultimately your choice.
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[@Thofte]

What if the boundary violator is a family member. But ending the relationship with the boundary violator probably means ending the relationship with several other family members, that I like/have no problem with. Or if it is some stranger in public, where I don't have a relationship that could be ended to begin with.

[@jasonmillercoaching4578]

These are your decisions to make. No one can tell you what to do. But strangers are not in a relationship with you by definition. So if they do something unacceptable to you, you just don't initiate a relationship.

[@Thofte]

@@jasonmillercoaching4578 Ok, I get the first part of your answer. Thanks for clearing it up. What I was trying to say with the stranger example is this: When family members violate my boundaries, I can threaten to end the relationship. That gives me some basis to negotiate on. But how can I set boundaries with total strangers ? Since I'm not in a relationship with them I have no leverage.

[@jasonmillercoaching4578]

@@Thofte Strangers you can walk away from forever if they do something you don't like. But you can't make someone do something they don't want to do.